Spectral Graph Clustering

Spectral clustering is a powerful technique in data analysis that has found increasing support and application in many areas. This report is geared to give an introduction to its methods, presenting the most common algorithms, discussing advantages and disadvantages of each, rather than endorsing one of them as the best, because, arguably, there is no black-box algorithm, which performs equally well for any data. We present results from previous studies and conclude that methods based on Ncut and multiway are most promising for general application.

[1]  Marina Meila,et al.  A Comparison of Spectral Clustering Algorithms , 2003 .

[2]  J. H. Ward.  Hierarchical Grouping to Optimize an Objective Function , 1963 .

[3]  Tao Jiang,et al.  Algorithmic Approaches to Clustering Gene Expression Data , 2002 .

[4]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[5]  Roded Sharan,et al.  Algorithmic approaches to clustering gene expression data , 2001 .

[6]  Marina MeWi.  Comparing Clusterings , 2002 .

[7]  Andrew W. Moore,et al.  The Anchors Hierarchy: Using the Triangle Inequality to Survive High Dimensional Data , 2000, UAI.

[8]  Ulrike von Luxburg,et al.  A tutorial on spectral clustering , 2007, Stat. Comput..

[9]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[10]  Carla E. Brodley,et al.  Feature Selection for Unsupervised Learning , 2004, J. Mach. Learn. Res..

[11]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[12]  Michael I. Jordan,et al.  On Spectral Clustering: Analysis and an algorithm , 2001, NIPS.

[13]  Santosh S. Vempala,et al.  On clusterings-good, bad and spectral , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[14]  B. Mohar.  Some applications of Laplace eigenvalues of graphs , 1997 .

[15]  Jianbo Shi,et al.  A Random Walks View of Spectral Segmentation , 2001, AISTATS.

[16]  Jianbo Shi,et al.  Learning Segmentation by Random Walks , 2000, NIPS.

[17]  Andrew B. Kahng,et al.  New spectral methods for ratio cut partitioning and clustering , 1991, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[18]  S H Strogatz,et al.  Random graph models of social networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.